Radial tree

Example of a radial tree, from a 1924 organization chart that emphasizes a central authority[1]

A radial tree, or radial map, is a method of displaying a tree structure (e.g., a tree data structure) in a way that expands outwards, radially. It is one of many ways to visually display a tree,[2][3] with examples extending back to the early 20th century.[4] In use, it is a type of information graphic.

Radial vs. triangular tree layout

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In a simple case, the first node is at the top, and the linked nodes are beneath. As each node typically has more than one child, the resulting shape is relatively triangular. In a radial layout, instead of each successive generation being displayed a row below, each generation is displayed in a new, outer orbit.

Since the length of each orbit increases with the radius, there tends to be more room for the nodes. A radial tree will spread the larger number of nodes over a larger area as the levels increase. We use the terms level and depth interchangeably.[5] Nevertheless, the number of nodes increases exponentially with the distance from the first node, whereas the circumference of each orbit increases linearly, so, by the outer orbits, the nodes tend to be packed together.

The overall distance "d" is the distance between levels of the graph. It is chosen so that the overall layout will fit within a screen. Layouts are generated by working outward from the center, root. The first level is a special case because all the nodes have the same parent. The nodes for level 1 can be distributed evenly, or weighted depending on the number of children they have. For subsequent levels, the children are positioned within sectors of the remaining space, so that child nodes of one parent do not overlap with others.

There are many extensions to this algorithm to create more visually balanced layouts, to allow a user to navigate from node to node (changing the center),[6] or accommodate node labels and mix force-directed layouts with radial layouts.[7]

The layout has some similarities to a hyperbolic tree, though a key difference is that hyperbolic trees are based on hyperbolic geometry, whereas in a radial tree the distance between orbits is relatively linear.

1.
Tree structure
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A tree structure or tree diagram is a way of representing the hierarchical nature of a structure in a graphical form. A tree structure is conceptual, and appears in several forms, for a discussion of tree structures in specific fields, see Tree for computer science, insofar as it relates to graph theory, see tree, or also tree. Other related pages are listed below, the tree elements are called nodes. The lines connecting elements are called branches, nodes without children are called leaf nodes, end-nodes, or leaves. Every finite tree structure has a member that has no superior and this member is called the root or root node. The root is the starting node, but the converse is not true, infinite tree structures may or may not have a root node. The names of relationships between nodes model the kinship terminology of family relations, the gender-neutral names parent and child have largely displaced the older father and son terminology, although the term uncle is still used for other nodes at the same level as the parent. A nodes parent is a one step higher in the hierarchy. Sibling nodes share the same parent node, a nodes uncles are siblings of that nodes parent. A node that is connected to all nodes is called an ancestor. The connected lower-level nodes are descendants of the ancestor node, in the example, encyclopedia is the parent of science and culture, its children. Art and craft are siblings, and children of culture, which is their parent, also, encyclopedia, as the root of the tree, is the ancestor of science, culture, art and craft. Finally, science, art and craft, as leaves, are ancestors of no other node, the Oxford English Dictionary records use of both the terms tree structure and tree-diagram from 1965 in Noam Chomskys Aspects of the Theory of Syntax. In a tree there is one and only one path from any point to any other point. Computer science uses tree structures extensively For a formal definition see set theory, internet, usenet hierarchy Document Object Models logical structure, Yahoo. Almost always, these boil down to variations, or combinations, of a few basic styles, Classical node-link diagrams, nested sets that use enclosure/containment to show parenthood, examples include TreeMaps and fractal maps. Layered icicle diagrams that use alignment/adjacency, lists or diagrams that use indentation, sometimes called outlines or tree views. A correspondence to nested parentheses was first noticed by Sir Arthur Cayley, trees can also be represented radially

2.
Tree (data structure)
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Alternatively, a tree can be defined abstractly as a whole as an ordered tree, with a value assigned to each node. Both these perspectives are useful, while a tree can be analyzed mathematically as a whole, a tree is a data structure made up of nodes or vertices and edges without having any cycle. The tree with no nodes is called the null or empty tree, a tree that is not empty consists of a root node and potentially many levels of additional nodes that form a hierarchy. Root The top node in a tree, child A node directly connected to another node when moving away from the Root. Parent The converse notion of a child, siblings A group of nodes with the same parent. Descendant A node reachable by repeated proceeding from parent to child, ancestor A node reachable by repeated proceeding from child to parent. Leaf A node with no children, branch Internal node A node with at least one child. Degree The number of sub trees of a node, edge The connection between one node and another. Path A sequence of nodes and edges connecting a node with a descendant, level The level of a node is defined by 1 +. Height of node The height of a node is the number of edges on the longest path between that node and a leaf, height of tree The height of a tree is the height of its root node. Depth The depth of a node is the number of edges from the root node to the node. Forest A forest is a set of n ≥0 disjoint trees, there is a distinction between a tree as an abstract data type and as a concrete data structure, analogous to the distinction between a list and a linked list. To allow finite trees, one must either allow the list of children to be empty, or allow trees to be empty, in case the list of children can be of fixed size. As a data structure, a tree is a group of nodes, where each node has a value. This data structure actually defines a graph, because it may have loops or several references to the same node. Thus there is also the requirement that no two references point to the node, and a tree that violates this is corrupt. For example, rather than an empty tree, one may have a reference, a tree is always non-empty. In fact, every node must have one parent

3.
Infographic
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Information graphics or infographics are graphic visual representations of information, data or knowledge intended to present information quickly and clearly. They can improve cognition by utilizing graphics to enhance the human visual system’s ability to see patterns, similar pursuits are information visualization, data visualization, statistical graphics, information design, or information architecture. Infographics have evolved in recent years to be for mass communication, Isotypes are an early example of infographics conveying information quickly and easily to the masses. Infographics have been around for years and recently the increase of a number of easy-to-use. Social media sites such as Facebook and Twitter have also allowed for individual infographics to be spread among people around the world. Infographics are widely used in the age of short attention span, in newspapers, infographics are commonly used to show the weather, as well as maps, site plans, and graphs for summaries of data. Some books are almost entirely made up of information graphics, such as David Macaulays The Way Things Work, the Snapshots in USA Today are also an example of simple infographics used to convey news and current events. Public transportation maps, such as those for the Washington Metro, public places such as transit terminals usually have some sort of integrated signage system with standardized icons and stylized maps. Indeed graphics can be more precise and revealing than conventional statistical computations, in 1626, Christoph Scheiner published the Rosa Ursina sive Sol, a book that revealed his research about the rotation of the sun. Infographics appeared in the form of demonstrating the Sun’s rotation patterns. In 1786, William Playfair, an engineer and political economist, to represent the economy of 18th Century England, Playfair used statistical graphs, bar charts, line graphs, area charts, and histograms. In his work, Statistical Breviary, he is credited with introducing the first pie chart, around 1820, modern geography was established by Carl Ritter. His maps included shared frames, agreed map legends, scales, repeatability, such a map can be considered a supersign which combines sign systems—as defined by Charles Sanders Peirce—consisting of symbols, icons, indexes as representations. Other examples can be seen in the works of geographers Ritter and Alexander von Humboldt, in 1857, English nurse Florence Nightingale used information graphics to persuade Queen Victoria to improve conditions in military hospitals. The principal one she used was the Coxcomb chart, a combination of stacked bar and pie charts, depicting the number,1861 saw the release of an influential information graphic on the subject of Napoleons disastrous march on Moscow. James Joseph Sylvester introduced the term graph in 1878 in the scientific magazine Nature and these were also some of the first mathematical graphs. The Cologne Progressives developed an approach to art which focused on communicating information. Here simple images were used to represent data in a structured way, following the victory of Austrofascism in the Austrian Civil War, the team moved to the Netherlands where they continued their work rebranding it Isotypes

4.
Force-directed graph drawing
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Force-directed graph drawing algorithms are a class of algorithms for drawing graphs in an aesthetically pleasing way. While graph drawing can be a problem, force-directed algorithms, being physical simulations. Force-directed graph drawing algorithms assign forces among the set of edges, in equilibrium states for this system of forces, the edges tend to have uniform length, and nodes that are not connected by an edge tend to be drawn further apart. Minimizing the difference between Euclidean and ideal distances between nodes is then equivalent to a metric multidimensional scaling problem, a force-directed graph can involve forces other than mechanical springs and electrical repulsion. Analogues of magnetic fields may be used for directed graphs, repulsive forces may be placed on edges as well as on nodes in order to avoid overlap or near-overlap in the final drawing. In drawings with curved edges such as circular arcs or spline curves, forces may also be placed on the points of these curves. Once the forces on the nodes and edges of a graph have been defined, in such a simulation, the forces are applied to the nodes, pulling them closer together or pushing them further apart. This is repeated iteratively until the system comes to an equilibrium state. The positions of the nodes in equilibrium are used to generate a drawing of the graph. It is also possible to employ mechanisms that search more directly for energy minima, such mechanisms, which are examples of general global optimization methods, include simulated annealing and genetic algorithms. This last criterion is among the most important ones and is hard to achieve any other type of algorithm. Flexibility Force-directed algorithms can be adapted and extended to fulfill additional aesthetic criteria. This makes them the most versatile class of graph drawing algorithms, examples of existing extensions include the ones for directed graphs, 3D graph drawing, cluster graph drawing, constrained graph drawing, and dynamic graph drawing. Intuitive Since they are based on physical analogies of common objects, like springs and this is not the case with other types of graph-drawing algorithms. Simplicity Typical force-directed algorithms are simple and can be implemented in a few lines of code, other classes of graph-drawing algorithms, like the ones for orthogonal layouts, are usually much more involved. Interactivity Another advantage of this class of algorithm is the interactive aspect, by drawing the intermediate stages of the graph, the user can follow how the graph evolves, seeing it unfold from a tangled mess into a good-looking configuration. In some interactive graph drawing tools, the user can pull one or more out of their equilibrium state. This makes them a choice for dynamic and online graph-drawing systems

5.
Hyperbolic tree
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A hyperbolic tree is an information visualization and graph drawing method inspired by hyperbolic geometry. Displaying hierarchical data as a tree suffers from visual clutter as the number of nodes per level can grow exponentially, for a simple binary tree, the maximum number of nodes at a level n is 2n, while the number of nodes for larger trees grows much more quickly. Drawing the tree as a node-link diagram thus requires exponential amounts of space to be displayed, one approach is to use a hyperbolic tree, first introduced by Lamping et al. Hyperbolic trees employ hyperbolic space, which intrinsically has more room than Euclidean space, displaying a hyperbolic tree commonly utilizes the Poincaré disk model of hyperbolic geometry, though the Klein-Beltrami model can also be used. Both display the hyperbolic plane within a unit disk, making the entire tree visible at once. The unit disk gives a fish-eye lens view of the plane, giving emphasis to nodes which are in focus. Traversing the hyperbolic tree requires Möbius transformations of the space, bringing new nodes into focus, hyperbolic trees have been patented in the U. S. by Xerox. Hyperbolic geometry Information visualization Radial tree – is also circular, Tree Tree The Green Tree of Life – Tree of life – University of California at Berkeley and Jepson Herbaria Tree of life Similar to the above, but with pictures

6.
Hyperbolic geometry
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In mathematics, hyperbolic geometry is a non-Euclidean geometry. Hyperbolic plane geometry is also the geometry of saddle surface or pseudospherical surfaces, surfaces with a constant negative Gaussian curvature, a modern use of hyperbolic geometry is in the theory of special relativity, particularly Minkowski spacetime and gyrovector space. In Russia it is commonly called Lobachevskian geometry, named one of its discoverers. This page is mainly about the 2-dimensional hyperbolic geometry and the differences and similarities between Euclidean and hyperbolic geometry, Hyperbolic geometry can be extended to three and more dimensions, see hyperbolic space for more on the three and higher dimensional cases. Hyperbolic geometry is closely related to Euclidean geometry than it seems. When the parallel postulate is removed from Euclidean geometry the resulting geometry is absolute geometry, there are two kinds of absolute geometry, Euclidean and hyperbolic. All theorems of geometry, including the first 28 propositions of book one of Euclids Elements, are valid in Euclidean. Propositions 27 and 28 of Book One of Euclids Elements prove the existence of parallel/non-intersecting lines and this difference also has many consequences, concepts that are equivalent in Euclidean geometry are not equivalent in hyperbolic geometry, new concepts need to be introduced. Further, because of the angle of parallelism hyperbolic geometry has an absolute scale, single lines in hyperbolic geometry have exactly the same properties as single straight lines in Euclidean geometry. For example, two points define a line, and lines can be infinitely extended. Two intersecting lines have the properties as two intersecting lines in Euclidean geometry. For example, two lines can intersect in no more than one point, intersecting lines have equal opposite angles, when we add a third line then there are properties of intersecting lines that differ from intersecting lines in Euclidean geometry. For example, given 2 intersecting lines there are many lines that do not intersect either of the given lines. While in some models lines look different they do have these properties, non-intersecting lines in hyperbolic geometry also have properties that differ from non-intersecting lines in Euclidean geometry, For any line R and any point P which does not lie on R. In the plane containing line R and point P there are at least two lines through P that do not intersect R. This implies that there are through P an infinite number of lines that do not intersect R. All other non-intersecting lines have a point of distance and diverge from both sides of that point, and are called ultraparallel, diverging parallel or sometimes non-intersecting. Some geometers simply use parallel lines instead of limiting parallel lines and these limiting parallels make an angle θ with PB, this angle depends only on the Gaussian curvature of the plane and the distance PB and is called the angle of parallelism

7.
MindManager
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MindManager is a commercial mind mapping software application developed by Mindjet. The software provides ways for users to visualize information in mind maps, MindManager can be used to manage projects, organize information, and for brainstorming. As of December 2015, Mindjet had approximately two million users, including customers such as Dow, Microsoft, Pfizer, and Cisco. MindManager provides ways for users to visualize information using mind maps, the digital mind maps can be used as a “virtual whiteboard” for brainstorming, managing and planning projects, compiling research, organizing large amounts of information, and for strategic planning. MindManager also has features that allow budget calculations and formulas, Gantt chart views of project timelines, documents can be attached to mind map topics and viewed within the MindManager application. Links, images, and notes can also be added to mind map topics, the software that became MindManager was originally developed by Mike Jetter in the mid-1990s while he was recovering from a bone marrow transplant to treat leukemia. Jetters goal was to develop a program that would overcome the limitations of creating maps with pen and paper. Following his release from hospital, Jetter decided to sell the software, the softwares mind maps were initially based on the method created by Tony Buzan. Over time, however, Mindjet has developed its own style of mind mapping, the software was originally marketed under the name MindMan — The Creative MindManager. In 1999, it was rebranded as MindManager, originally only available for Windows, MindManager expanded to Mac OS X in 2006. With the release of version 7, the Windows version of MindManager adopted the ribbon interface first seen in Microsoft Office 2007, in 2011, mobile versions of MindManager were released for both iOS and Android. In September 2012, the Mindjet company combined all of its software, including MindManager, Mindjet Connect, Mindjet moved away from the single-product offering in mid-2013. The stand-alone mind mapping product was again named MindManager, with an expansive version tailored to large enterprise adoptions called MindManager Enterprise released in 2014. MindManager Enterprise added sharing options including viewing/editing within Microsoft SharePoint, a MindManager mind map viewer also became available with MindManager Enterprise 2016. On August 9,2016, Corel announced that they had acquired the Mindjet MindManager business, MindManager has received generally positive notice from reviewers. MindManager 2016 for Windows took first place in Biggerplates MindMappers Choice poll, MindManager 8 received four out of five stars from TechRadar, while MindManager 9 received 3.5 out of 5 stars from PC Magazine and 4 out of 5 stars from Macworld. MindManager was chosen as one of the top 5 best mind mapping tools, brainstorming List of concept- and mind-mapping software Official website

8.
MindMapper
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MindMapper offers integration with Microsoft Office and Unicode support. Dashboard is bird’s-eye view the past, present and future activities, the visual map is a project blueprint that facilitates ideation and collaboration. The Planner is a management tool that fosters project execution. MindMapper was first developed as an tool to help with industrial simulation projects for SimTech Systems in 1997. 2014, MindMapper 14 Dec.2015, MindMapper 16 with Planner and Mapper Jan

9.
Mind map
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A mind map is a diagram used to visually organize information. A mind map is hierarchical and shows relationships among pieces of the whole. It is often created around a concept, drawn as an image in the center of a blank page, to which associated representations of ideas such as images, words. Major ideas are connected directly to the concept, and other ideas branch out from those. Mind maps can be drawn by hand, either as rough notes during a lecture, meeting or planning session, for example, Mind maps are considered to be a type of spider diagram. A similar concept in the 1970s was idea sun bursting, some of the earliest examples of such graphical records were developed by Porphyry of Tyros, a noted thinker of the 3rd century, as he graphically visualized the concept categories of Aristotle. Philosopher Ramon Llull also used such techniques, the semantic network was developed in the late 1950s as a theory to understand human learning and developed further by Allan M. Collins and M. Ross Quillian during the early 1960s. Mind maps are similar in structure to concept maps, developed by learning experts in the 1970s. Buzans specific approach, and the introduction of the mind map arose during a 1974 BBC TV series he hosted, called Use Your Head. In this show, and companion series, Buzan promoted his conception of radial tree, diagramming key words in a colorful, radiant. Buzan says the idea was inspired by Alfred Korzybskis general semantics as popularized in science fiction novels, such as those of Robert A. Heinlein and A. E. van Vogt. He argues that while traditional outlines force readers to scan left to right and top to bottom, Buzan suggests the following guidelines for creating mind maps, Start in the center with an image of the topic, using at least 3 colors. Use images, symbols, codes, and dimensions throughout your mind map, select key words and print using upper or lower case letters. Each word/image is best alone and sitting on its own line, the lines should be connected, starting from the central image. The lines become thinner as they radiate out from the center, make the lines the same length as the word/image they support. Use multiple colors throughout the map, for visual stimulation. Develop your own style of mind mapping. Use emphasis and show associations in your mind map, keep the mind map clear by using radial hierarchy or outlines to embrace your branches